Local and global behaviour of nonlinear equations with natural growth terms

This paper concerns a study of the pointwise behaviour of positive solutions to certain quasi-linear elliptic equations with natural growth terms, under minimal regularity assumptions on the underlying coefficients. Our primary results consist of optimal pointwise estimates for positive solutions of such equations in terms of two local Wolff's potentials.Comment: In memory of Professor Nigel Kalto

Manin matrices and Talalaev's formula

We study special class of matrices with noncommutative entries and demonstrate their various applications in integrable systems theory. They appeared in Yu. Manin's works in 87-92 as linear homomorphisms between polynomial rings; more explicitly they read: 1) elements in the same column commute; 2) commutators of the cross terms are equal: $[M_{ij}, M_{kl}]=[M_{kj}, M_{il}]$ (e.g. $[M_{11}, M_{22}]=[M_{21}, M_{12}]$). We claim that such matrices behave almost as well as matrices with commutative elements. Namely theorems of linear algebra (e.g., a natural definition of the determinant, the Cayley-Hamilton theorem, the Newton identities and so on and so forth) holds true for them. On the other hand, we remark that such matrices are somewhat ubiquitous in the theory of quantum integrability. For instance, Manin matrices (and their q-analogs) include matrices satisfying the Yang-Baxter relation "RTT=TTR" and the so--called Cartier-Foata matrices. Also, they enter Talalaev's hep-th/0404153 remarkable formulas: $det(\partial_z-L_{Gaudin}(z))$, det(1-e^{-\p}T_{Yangian}(z)) for the "quantum spectral curve", etc. We show that theorems of linear algebra, after being established for such matrices, have various applications to quantum integrable systems and Lie algebras, e.g in the construction of new generators in $Z(U(\hat{gl_n}))$ (and, in general, in the construction of quantum conservation laws), in the Knizhnik-Zamolodchikov equation, and in the problem of Wick ordering. We also discuss applications to the separation of variables problem, new Capelli identities and the Langlands correspondence.Comment: 40 pages, V2: exposition reorganized, some proofs added, misprints e.g. in Newton id-s fixed, normal ordering convention turned to standard one, refs. adde

Dual Mode of Mitochondrial ROS Action during Reprogramming to Pluripotency

Essential changes in cell metabolism and redox signaling occur during the reprogramming of somatic cells into induced pluripotent stem cells (iPSCs). In this paper, using genetic and pharmacological approaches, we have investigated the role of electron transport chain (ETC) complex-I (CI) of mitochondria in the process of cell reprogramming to pluripotency. Knockdown of NADH-ubiquinone oxidoreductase core subunits S1 (Ndufs1) or subunit B10 (Ndufb10) of the CI or inhibition of this complex with rotenone during mouse embryonic fibroblast (MEF) reprogramming resulted in a significantly decreased number of induced pluripotent stem cells (iPSCs). We have found that mitochondria and ROS levels due course of the reprogramming tightly correlate with each other, both reaching peak by day 3 and significantly declining by day 10 of the process. The transient augmentation of mitochondrial reactive oxygen species (ROS) could be attenuated by antioxidant treatment, which ameliorated overall reprogramming. However, ROS scavenging after day 3 or during the entire course of reprogramming was suppressive for iPSC formation. The ROS scavenging within the CI-deficient iPSC-precursors did not improve, but further suppressed the reprogramming. Our data therefore point to distinct modes of mitochondrial ROS action during the early versus mid and late stages of reprogramming. The data further substantiate the paradigm that balanced levels of oxidative phosphorylation have to be maintained on the route to pluripotency

Positioning of Chromosomes in Human Spermatozoa Is Determined by Ordered Centromere Arrangement

<div><p>The intranuclear positioning of chromosomes (CHRs) is a well-documented fact; however, mechanisms directing such ordering remain unclear. Unlike somatic cells, human spermatozoa contain distinct spatial markers and have asymmetric nuclei which make them a unique model for localizing CHR territories and matching peri-centromere domains. In this study, we established statistically preferential longitudinal and lateral positioning for eight CHRs. Both parameters demonstrated a correlation with the CHR gene densities but not with their sizes. Intranuclear non-random positioning of the CHRs was found to be driven by a specific linear order of centromeres physically interconnected in continuous arrays. In diploid spermatozoa, linear order of peri-centromeres was identical in two genome sets and essentially matched the arrangement established for haploid cells. We propose that the non-random longitudinal order of CHRs in human spermatozoa is generated during meiotic stages of spermatogenesis. The specific arrangement of sperm CHRs may serve as an epigenetic basis for differential transcription/replication and direct spatial CHR organization during early embryogenesis.</p> </div

Localization of chromosome territories in human spermatozoa.

<p>(A) A typical image of chromosome territories in spermatozoa obtained using FISH with WCP probes. HSA18 paint – red, HSA3 – green, total DNA stained with DAPI – blue. (B) The scheme explaining the determination of CT center coordinates following FISH. The apical end of the ellipsoid sperm cell is on the left (<b><i>x</i></b> = 0), the tail (green) attachment point - on the right. (C) Examples of the statistical evaluation of chromosome positioning. Position of each CT was determined in ≥80 cells. Left - contour plots showing the probability to find the CT center within the given area of the nucleus (red – the most probable localization). The color-coded bar at the bottom of the figure represents the p-value, with the red indicating p≤0.125 (the most probable localization) and the navy 0.875≤p≤1.000. The central and the right panels – frequency distribution plots for the longitudinal (along the long nuclear axis) and the lateral (along the short nuclear axis) positioning, respectively. Scale bar – 5 µm.</p

Relation between chromosome properties and their intranuclear localization in spermatozoa.

<p>(A) Examples of the CHR longitudinal coordinate determination using the Gaussian approximation (red line) of the frequency distribution data (black line). Numerical values of longitudinal (B) and lateral (D) coordinates of the CT centers. Correlations between the longitudinal (C) or the lateral (E) chromosome positioning and densities of coding sequences (left panels) or the chromosome size (right panels). <b><i>x</i></b> – the distance from the apical end of the sperm nuclei, <b><i>h</i></b> – the distance between the CT center and the long nuclear axis as described in the scheme <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0052944#pone-0052944-g001" target="_blank">Fig. 1,B</a>.</p

In human spermatozoa, nonhomologous centromeres are arranged in arrays with the fixed chromosome-specific linear order.

<p>(A) Visualization of CEN arrays using FISH with pan-CEN DNA probe. Nucleus borders, determined by DAPI staining are shown by a blue dashed line. (B) The outline of the sequential FISH procedure. First, cells were hybridized with pan-CEN probe (a, green). Cells that demonstrated unfolded CEN strings were subjected to sequential FISH with chromosome-specific peri-CEN probes (b–e). (f) - Artificial colors were assigned to the peri-CEN signals and images were merged. (g) - Schematic representation of the chromosome-specific peri-CEN localization. (C) Examples of CEN localization along sperm chromocenter arrays. (D) The cumulative scheme. (E) The order of CENs is preserved in diploid sperm nuclei. (a) Diploid sperm cells revealed using FISH with chromosome-specific peri-CEN probes; merged images after sequential FISH. (b) - Schematic representation of chromosome-specific peri-CEN localization. (c) - Cumulative scheme. Noteworthy, two sets of chromosomes have the same linear order matching with the arrangement established in haploid sperm nuclei (D). Scale bars in A–E – 5 µm.</p

Model of chromosome organization in human spermatozoa.

<p>Compact CTs (filled contours) have overall hairpin conformations (chromosome paths indicated by dashed lines) with the <i>p</i> and <i>q</i> telomere/sub-telomere domains (orange circles) forming dimers at nuclear periphery. Gene-rich CHRs – rosy, gene-poor – indigo. CTs are connected via centromeres/peri-centromeres (green circles and lines) into arrays and have a fixed linear order which determines the longitudinal positioning of chromosomes.</p